It is often necessary to take a regular set of samples representing a scanned image and convert them to a smaller number of samples which represent the same image. A typical example is the conversion of a high-definition TV picture into an equivalent standard-definition picture. The process is usually carried out separately in the horizontal and vertical dimensions; the horizontal process reducing the number of samples per line, and the vertical process reducing the number of scan lines. Temporal sub-sampling is also possible to reduce the rate at which successive pictures are output.
Where the samples are represented as a sequence of values in a digital system, it is well known to use a finite impulse response (FIR) digital filter of the form shown in FIG. 1 to decimate the samples. Referring to FIG. 1 (in which the parameter D represents the required decimation factor), a sequential stream of samples (1) is input to a set of cascaded delay elements (2). Each of the individual delay elements has a delay equal to the product of the required decimation factor and the input sample period. (Typically these delays take the form of a set of registers controlled by a common clock signal which causes the sample values to propagate along the “pipeline” of registers.) Samples equally spaced along the set of delays are input to a set of multipliers (3) which multiply each sample by a coefficient value sent to the respective multiplier from a control system (4), and the outputs of the multipliers are summed (5). Once per input sample the sum is added to the contents of an accumulator (6). After a number of accumulations equal to the decimation factor, the accumulated value is output as a decimated sample (7), the accumulator set to zero and the process repeats to produce the next decimated sample.
The set of multiplier coefficients which are used to construct a particular decimated output sample are known as the filter “aperture” and there are well-known methods for deriving them. For large decimation factors, it is usually advantageous to have a “wide” filter aperture including weights for a large number of input samples; for a given decimation factor increasing the width of the aperture requires an increase in the number of multipliers and delay elements.
In this prior-art system it is difficult to vary the decimation factor. A first problem arises since the delays between the multiplier inputs have to be changed to match the factor. Also, for very large decimation factors, correspondingly long delays are required. This is particularly difficult when decimating vertically, as vertically-adjacent samples are separated by the number of samples per line and the delays have to be increased by this factor.